A novel multi-objective co-evolutionary algorithm based on decomposition approach

Abstract

Recently, co-evolution mechanism is exploited to solve multi-objective optimization problems by using multiple subpopulations on a cooperative manner, such as co-evolutionary multi-swarm particle swarm optimization (CMPSO) based on the multiple subpopulations for multi-objective optimization (MPMO) framework, which is also extended to cooperative multi-objective differential evolution (CMODE). Although their approaches of optimizing each objective with each subpopulation are effective, the evolution and selection methods conducted on external archive are also important for co-evolution, as they significantly impact a lot on the quality and the distribution of final solutions. In this paper, we present a novel multi-objective co-evolutionary algorithm based on decomposition approach (MCEA), also using the subpopulation to enhance each objective. A more powerful DE operator with an adaptive parameters control is run on both of multiple subpopulations and external archive, which helps to improve each objective and diversify the tradeoff solutions on external archive. Moreover, computational resource assignment is also realized between each subpopulation and external archive. Once one objective stops to be enhanced, this objective may find its optimal value and more computational resource can be assigned to evolve other objectives and external archive. By this way, the tradeoff between all the objectives can be well balanced and external archive also has more opportunities for evolution. After evaluating the proposed algorithm on 31 benchmark test problems, such as the ZDT, DTLZ, WFG, UF series problems, the experimental results show that MCEA presents some advantages over two co-evolutionary algorithms (i.e., CMPSO and CMODE) and several state-of-the-art multi-objective evolutionary algorithms (i.e., NSGA-II, SPEA2, MOEA/D-DE, MOEA/D-STM, MOEA/D-FRRMAB and MOEA/D-IR).